System Definition and 1000 Threads

Hey! :o We have the basis $B=\left \{\begin{pmatrix}1 \\ 1 \\ 1\end{pmatrix},\begin{pmatrix}2 \\ 1 \\ 0\end{pmatrix}, \begin{pmatrix}1 \\ 2 \\ 1\end{pmatrix} \right \}$ of $\mathbb{R}^3$ and the vector $v$ can we written as a linear combination of the elements of the basis as follows...

Hello, $\vec{x'}=\small\begin{pmatrix}1&2\\3&2\end{pmatrix}\vec{x}+t\small\begin{pmatrix}2\\-4\end{pmatrix}$ Now i got the solution to this differential equation system as...

Homework Statement [please see attached photo] Homework Equations [please see attached photo] The Attempt at a Solution [please see attached photo] The issue for me starts with (but probably doesn't end with) replicating the velocity equation using the Conservation of Energy equations. Is...

Hi All. I'm new here so I hope you will bear with me and please tell me if this is out of context or in the wrong part of the forum. I am trying to programm a falling pipe system with corners in ArchiCAD (GDL). I have been programming in different languages for a while now, but new to 3D vector...

Homework Statement I'm having trouble worki out the transfer function of the block. Whats confusing me is the input of O2 input of 50. If that wasn't there I know the transfer function would be Oo/Oi=G/1+GH. Homework EquationsThe Attempt at a Solution

Let, we want to calculate the P.E(potential energy) of a system containing 3particles p1,p2,p3.the point of observation is P.so now we should add up the P.E at P due to p1,p2,p3 to get the net potential energy of the system,but why we take the P.E of particles due to each other into count...

If I have a tank half-filled with low boiling point liquid at ambient temperature, then this tank is placed inside dry oven whose temperature is kept to be around 5℃ above the liquid boiling temperature. A fan is placed inside the dry oven as an effort to make temperature distribution even or at...

Homework Statement Homework Equations and the attempt at a solution[/B] Approach: Use the solution for the damped oscillating system provided in the formula sheet. We must use the given initial conditions to find the unknown phase ##\phi## and that will give us an expression for ##x## in...

Homework Statement Give an example of a non-linear discrete-time system of the form x1(k + 1) = f1(x1(k), x2(k)) x2(k + 1) = f2(x1(k), x2(k)) With precisely four singular points, two of which are unstable, and two other singular points which are asymptotically stable. Homework Equations J =...

Find x, y, z solving all the three equations: y^2 + (y*x) - z - x = 0z^2 + (z*y) - x - y = 0x^2 + (x*z) - y - z = 0I would be very grateful!

In Summary: I have a test Friday in modeling mass-spring-pulley systems, and I'm struggling to tie everything together. We're using the textbook System Dynamics 3rd Edition by William Palm III, and while it does a great job describing the individual components of each system, it does a crappy...

I'm having trouble understanding the forces involved when defining the equation of motion for this particular problem. So... I've seen the answer for the eq. of motion worked two different ways. The first way involves combining the spring series into Keq = K1⋅K2/(K1+K2). The answer, plugging...

I'm a former physics student and I've been thinking about an interesting problem that eventually led me to the following thought experiment that I'm having trouble resolving. Imagine a two-compartment system, where one compartment is filled with He gas, and the other is filled with standard...

Homework Statement [/B] ##m=3kg## ##M=2kg## Coefficient of static friction between m and M ##\mu_1 = 0.6## Coefficient of static friction between M and the ground ##\mu_2 = 0.8##. The rope is weightless, does not stretch, and the wheel is frictionless. What is the maximum force ##F## that...

Homework Statement Determine the parameters of the PI controller such that two of the closed-loop poles of the transfer function Gclr(s) correspond to the poles of a second order LTI system with the following specifications: i) overshoot S% = 25%; and ii) settling time ts(5%) = 120 s. Homework...

Homework Statement 2. Relevant equationThe Attempt at a Solution ...[/B] Part c) I'm confused as to how the actual pulley system works. If its balanced wouldn't it be stationary. How does it move? I thought that since its balanced the acceleration of the system is constant and therefore to...

Homework Statement A mass m1 is located on a platform with mass M. The platfrom is located on springs with total constant k such that it can swing vertically in direction x. a) Write down the equations of motion assuming mass m1 will always be connected to the platform. Write it as x(t) b)...

Homework Statement This is Rankine-Hugoniot conditions at a hydrodynamic shock front. Where P2=0 v2=0. The problem is attached. I need to solve a system of equations. I thought it would be relatively straight forward solving for the three unknowns but I'm struggling. I know it's possible to...

Hi all, I was working on a problem using Euler-Lagrange equations, and I started wondering about the total and partial derivatives. After some fiddling around in equations, I feel like I have confused myself a bit. I'm not a mathematician by training, so there must exist some terminology which...

First time in this forum, so greetings to everyone! I am currently working with some physical models in the field of natural ventilation and I came across the following 5th order polynomial equation (quintic function): $X^{5}+ C X - C =0$ This is the steady state solution of a physical system...

I am confused with this concept. So if a system possesses multiple possible eigenfrequencies (and therefore modes), how does the system "know" which eigenfrequency will it want to vibrate on? Does that depend on the initial condition you give the system? Is there any mathematical relation...

Hello! (Wave) I want to solve the following system of congruences: $$x \equiv 13 \pmod{40} \\ x\equiv 5 \pmod{44} \\ x \equiv 38 \pmod{275}.$$I have thought the following: $$x \equiv 13 \pmod{40} \Leftrightarrow x \equiv 13 \pmod{2^3 \cdot 5}$$ $$x \equiv 5 \pmod{44} \Leftrightarrow x \equiv...

<Moderator's note: Moved from another forum and thus no template.> I have a project from my Mechanics class which consist on building the system on the picture. It has a spring, cable and a protractor. I have to do an approximation of the mass and weight of the object that is put in the...

I would really appreciate if someone could advise me whether the system below is a scleronomic or a rheonomic mechanical system, or a mix of both. If we consider the first pendulum, the constraint is fixed which leads to a scleronomous case while the constraint of the second pendulum is not...

So Pearson is telling me that, basically, the ratio of internal to external forces and the briefness of the time interval is what determines whether the external forces on a system whose momentum we're studying will affect whether we can obtain a decent approximation of the momenta of the...

Homework Statement A wireless communications system can achieve a theoretical maximum data rate of 200 Mbps using 16-QAM modulation in a 10 MHz channel and using a single spatial stream. What data rate could theoretically be achieved if the same system used 256-QAM and 8 spatial streams in a 20...

Homework Statement two blocks of masses 8kg and 4kg respectively are connected by a string as shown in firgure. calculate their accelerations if they are initially at rest on the floor. after a force of 100N is applied on the pulley in the upward direction (g=10 m/s). Homework Equations Σf=ma...

Homework Statement two blocks of mass m sit on a frictionless surface and are connected by a massless, unstrechable string that rolls on a massless, frictionless pulley as shown. the second mass sits on an inclined tipped at an angle θ relative to horizontal. at time t=0, both masses are...

Homework Statement An object is 25.0 cm to the left of a lens with a focal length of + 15 .0 cm. A second lens of focal length +15.0 cm is 30.0 cm to the right of the first lens. Find the location of the final image and draw it out. Homework Equations 1/f = 1/di + 1/do The Attempt at a...

Homework Statement The following figure represent the traversal cut of a system with two cylindrical equal conductors of radius r0 length l at a distance d from one another and at the same distance h of a plane conductor (conductor zero). The dielectric that surrounds the conductors is the air...

Homework Statement FIGURE 3 shows an open loop system containing a distance velocity lag and a single transfer lag. Figure 3 shows - Xi Xo ---->----[Distance - velocity lag of...

Homework Statement Two blocks of the masses m1=7.40 kg and m2=m1/2 are connected via a massless pulley and massless string. The system is currently in equilibrium but is about to start sliding, if m2 would increase even by a bit. For the friction between the surface and m1 assume that µs=µk...

Homework Statement A capacitor is made up of a pair of square plates, each of side length L, that are very nearly parallel (such that θ is very small) and separated by a distance D. The plates make an angle, θ, with one another. The capacitor may be thought of as being comprised of many...

Homework Statement If an amount of $1000 is deposited in a savings account that pays 3.2% interest per year compounded monthly, the amount in the account after nmonths is given by: The amount in the account after 2 years (rounded to one decimal point) will be??

Homework Statement I have a small question about the following problem. The figure represents the cross-section of a three-conductor system comprising a communications coaxial cable of length l running parallel to a conducting wall (reference conductor). Determine the partial capacitance scheme...

What will happen if a pathogen invades us and our immune system is completely ignorant about it or sleeping? Let us suppose it fails to identify the intruders. Can the consequences be explained pathophysiologically by taking any germ as an example? I want to know how a pathogen causes...

Hi there! I am currently making a design about drive systems used for micro-hydro scheme. I don't know what type of driving element is suitable to used for transmitting the power from a turbine (cross flow turbine) to a generator. I'm planning to use both chain and sprocket & V-Belt Pulley which...

Hi, I learned about how PE = U=kq1q2/r is the electrical potential energy for the system. It is found by taking the integral of electrical force and dr from infinity to the point of location we are interested in. So that is the intregral(F*dr) from r=inf to r=ro. My question is that do I...

The Question is posted as a photograph with a. little change. One of the mass in the photo is equal to '2m' rather than 'm'. Now the block won't stop consecutively. How would we approach the question?

Hello, For example, an electric field vector, such as the gradient of the potential, passes in the following way to any coordinate system:$$E = -\triangledown{}V = - \frac{{\partial V}}{{\partial x^i}}g^{ij}e_j$$ But what about a vector of a magnetic field? How would it be expressed in any...

If a wave function could be assigned to a whole galaxy, would its mass spread along the wave? Could this account for the anomalies in our calculations for galactic spin?

Me and my friend want to make a strong as possible (made from permanent magnets) homemade metal separator for seeds. We are not good in the physics of such level, so we need consultation. We want to try neodymium magnets for our separator. We learned that magnetic flux density could be reached...

Homework Statement A load was put on the right side of a seesaw 0.6 meter from its center as shown, on the other side a force of 49N is applied perpendicular to the seesaw surface 1 meter from its center, the setup is tuned to an angle of 30 from the horizontal axis as shown. On the right...

1. The problem statement Consider the case of 10 oscillators and eight quanta of energy. Determine the dominant configuration of energy for this system by identifying energy configurations and calculating the corresponding weights. What is the probability of observing the dominant...

Homework Statement "Consider a system with three states, ##|1\rangle , |2\rangle ,|3\rangle ## with energies ##\hbar \omega_1 , \hbar \omega_2 , \hbar \omega_3 ##. the states are then separated by ##\hbar \omega_3 -\hbar \omega_1 = \hbar \omega_{13}## and ## \hbar \omega_3-\hbar \omega_2= \hbar...

Hey guys, some insight to the following problem I have here would be helpful. I need to see if a conveyor is worth upgraded (i.e. see what the output Tonne/per hour is) from a belt 745mm wide, idler pulley 800mm wide... to a 800mm belt and 850mm wide idler pulley. Lets assume the length of the...

I was just looking at indeterminate statics problems where you have a beam, three elastic wires (left, centre, and right that are holding it up), and some extra mass. (Just like example 5 in the notes below: http://fast10.vsb.cz/lausova/indeterm_all.pdf). I understand the method that was used to...

Homework Statement Sakurai, problem 1.11 A two-state system is characterized by the Hamiltonian $$ H = H_{11} | 1 \rangle \langle 1| + H_{22} | 2 \rangle \langle 2| + H_{12} \left[ | 1 \rangle \langle 2| + | 2 \rangle \langle 1| \right] $$ where ##H_{11}##, ##H_{22}##, and ##H_{12}## are real...

Homework Statement (Note: this is the last part of a longer problem, so I hope I won't miss anything important) We have a laser with 2 energy levels, so the emitted photons will have the energy ##\omega##. For this given energy there are ##m## states in which the photon can be, denoted...

A few years ago I read two pretty groundbreaking linguistic papers from the 90s arguing that natural languages are networks which can be conceptualized from the perspective of nonlinear dynamical systems theory, with a lexicon being a state space and grammatical rules being attractors in that...